Thermoplastic elastomers (thermoplastic vulcanizates) have been foamed both chemically and mechanically as disclosed in U.S. Pat. No. 5,070,111. A preferred mechanical foaming agent is water due to its low toxicity. These foams can have elongations to break up to about 200%.
Elastic thermoplastics can be chemically foamed but are not readily foamed mechanically such as with water.
Thermoplastic elastomers have been modified with random or block styrene copolymers as disclosed in U.S. Pat. No. 4,906,683.
Polyurethane foams have been popular due to the ability to make both rigid foams and elastic foams by changing the chemical composition of the urethane polymers. Although there may be some exceptions, generally urethane foams are not reprocessable.